Josephson junction is a fundamental component for exploring the exotic properties of superconducting materials and serves as a critical building block for future quantum computing. When biased with a constant voltage, the junction oscillates at a frequency precisely given by f = (2e/h)*V, where e is the electron charge and h is Planck’s constant—this is the ac Josephson effect. Under microwave irradiation, this quantum behavior produces quantized voltage steps, known as Shapiro steps, in the current-voltage curve. The voltage of these steps, Vn = (hf/2e)*n, is determined solely by the microwave frequency f and fundamental constants. In standard Josephson junctions, n is an integer number. However, fractional steps, such as n = 1/2, 1/3, 1/4, etc., have also been observed in various systems, serving as signatures of unconventional superconductivity, topological superconducting state, or complex junction structures. Early observations of half-integer Shapiro steps were mainly reported in conventional superconductor-normal metal-superconductor (SNS) junctions or in grain boundary junctions made from high-temperature superconductors such as YBa2Cu3O7. These fractional steps were primarily attributed to microscopic mechanisms, including multiple Andreev reflections, the formation of micro-shorts, or synchronized motion of vortices in wide junctions.
Recently, theoretical studies (Phys. Rev. B 98, 104515 (2018), Nature Physics 17, 519–524 (2021)) proposed that twisting and stacking two atomically thin cuprate layers by 45° could induce a topological superconducting state, with half-integer Shapiro steps being one of its key experimental signatures. In 2023, Zhao et al. (Science 382, 1422–1427 (2023)) reported both half-integer steps and Josephson diode effect in twisted Bi2Sr2CaCu2O8+x (Bi-2212) junctions, suggesting the possible emergence of a topological superconducting phase. This exotic topological state urgently requires further experimental verification, especially since topological superconductivity is regarded as a crucial pathway toward realizing high-temperature Majorana zero modes—core components for fault-tolerant topological quantum computers.
Recently, Y. Zhu et al. (National Science Review, nwaf569, 2025) systematically investigated the ac Josephson effect in Bi-2212 twist junctions with different twist angles (30°, 40°, and 45°). They found that well-defined half-integer steps do appear in 45° twisted junctions. However, these subtle half Shapiro steps vanish after several thermal cycles. Importantly, they demonstrated that fractional steps could be reproducibly generated by using two training protocols: (1) magnetic-field training—applying a small magnetic field (< 10 mT); (2) current training (current annealing)—applying a large bias current (~1mA-3mA) during cooldown. With current training, not only half-integer Shapiro steps but also other fractional steps, such as 1/3 and 2/3, were observed. Interestingly, after current training, prominent half-integer steps have also been exhibited in junctions with 30° and 40° at relatively high temperatures—outside the expected regime for topological superconductivity. These results strongly suggest that the observed fractional Shapiro steps likely originate from the high-order terms in the current-phase relation induced by external effects, rather than from an intrinsic topological superconducting state. The authors propose that the fractional Shapiro steps in twisted junctions are mediated by a mechanism involving trapped vortices.
This work provides comprehensive experimental protocols—thermal cycling, magnetic-field training, and current annealing—to reveal the stability and origin of half-integer Shapiro steps. Adopting such approaches will not only help distinguish intrinsic topological signatures from extrinsic field-induced phenomena but also provide standard framework for future related experiments.
This work was accomplished through close collaboration among the Beijing Academy of Quantum Information Sciences (BAQIS), Southern University of Science and Technology (SUST), Tsinghua University, and the Hefei National Laboratory.